[TYPES] models of untyped lambda calculus

[Rosu, Grigore]

Are there conventional models of untyped lambda calculus for which equational deduction with alpha+beta is *complete*?  By conventional models I mean ones where lambda and application are interpreted as functions.
The Hindley-Longo style models are complete but non-conventional.  On the other hand, graph models are conventional but incomplete.

Thank you,
Grigore